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The support of functions and distributions with a spectral gap. (English) Zbl 0577.42008
Given a set $$A\subset R$$, when can one find a distribution in S’(R) or a function in $$L^ p(R)$$, not identically zero and supported on A, whose Fourier transform vanishes on some nonempty open interval? This is a variant of a question of H. Dym which has been worked on by A. Beurling and L. deBranges. The present author discusses these matters and proves, among other things, a general uniqueness theorem for distributions supported on regularly distributed intervals and a general existence theorem for functions with small support and a spectral gap.
Reviewer: P.Milnes

##### MSC:
 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
##### Keywords:
Fourier transform; small support; spectral gap
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